Physiological changes in Klingons between Star Trek TOS and Star Trek TNG

Yes, the retcon reason is that the Klingons in the TOS serials were suffering from an artificially created virus intended to improve their physical abilities.

Per Memory Alpha

The Klingon augment virus was a modified form of Levodian flu that threatened to wipe out the Klingon race in the mid-22nd century. It was inadvertently created by Klingon researchers who were attempting to bio-engineer enhanced warriors using DNA from genetically-modified Human embryos left over from Earth's Eugenics Wars.

by the time of the new ST: TNG series, a cure had evidently been found and universally administered.

A cure to restore Klingons to their proper appearance was presumably found some time between 2268 and 2293, as Kang was seen as a smooth-headed Klingon in TOS: "Day of the Dove" and as a normal Klingon in VOY: "Flashback". The first time normal Klingons were seen on screen was in Star Trek: The Motion Picture set in the early-2270s.

This drastic change in appearance for Klingons was a bit of a running joke among fans during later series of Star Trek. The writers even acknowledged it during an episode of Deep Space Nine which sees Worf, among others, time-travel back into the original series episode The Trouble with Tribbles. When asked why those Klingons looked funny he curtly replies

We do not discuss it with outsiders.

Many fan theories popped up over the years to explain away the problem. Finally, though, we got a canon answer in Enterprise, specifically the episodes "Affliction" and "Divergence". If you want the whole story in all it's detail, I'd highly recommend watching the entire story arc (it also ties in with The Wrath of Khan among other things.)

The basic idea, though, is that the Klingons got ahold of the genetically engineered humans from the Eugenics Wars and tried to use them to create genetically engineered Klingons. Something went wrong, and a odd strain of the flu virus infected many of the subjects, changing their appearance. This mutated look remained in the Klingon gene pool for a while afterward. Eventually, a cure for the flu was found, but it was a while longer before they were able to reverse the effects.

The original explanations were:

1. They Always looked like that, the budget just didn't allow it. Don't pay attention to the man behind the curtain:

   Gene Roddenberry tried to explain the differences between The Motion Picture's Klingons and the original ones by saying that the original show had simply never had the budget and makeup technology to envision the species as it should have been seen, so the apparently new Klingons were just Klingons as they were always intended to have been. (Cinefantastique, Vol. 37, No. 2, p. 40)

2. Or that there are more than one kind of Klingon, like there are races of humans.

   He additionally contemplated, "Just as there are different races of humans, there are different races of Klingons, and the Klingons seen in Star Trek: The Motion Picture are not the same race as the ones we saw on the original series." Since Fred Phillips expected that the fans would wonder about how the Klingons could possibly have head ridges newly added to their faces, he and Roddenberry came up with the explanation of there being a variety of Klingon races, even before the release of The Motion Picture. Despite this, the transformation continued to be regarded as a mystery for decades to come. (Star Trek: Communicator issue 145, pp. 71-72)

This continued until after Roddenberry died and they decided several decades afterwards to change the reason for the TOS Klingon look.

Klingons have looked that way since The Motion Picture, long before TNG.

The budget and technology are the same reason Gorns also don't look like the TOS guy in a latex suit:

For a long time, it was acknowledged but rather explicitly 'not discussed with outsiders.'

It was later addressed in Enterprise as the result of a widespread attempt at genetic engineering - the subjects took on human characteristics and were sent to serve on the front lines of the Klingon Defense Forces circa-TOS, presumably to banish them from the gene pool.

More, as always with things Trek, can be found at Memory Alpha

There are now, also, additional explanations. Star Trek: Discovery takes place about 10 years before TOS. One of it's expansions is looking at Klingons before they reform an empire, in which they are scattered across 24 houses, most seemingly on different planets.

From Star Trek Movie.com

"The empire is very big. They don’t all grow up on Kronos. They don’t all live on the same planets and certainly those different planets would have different environments. So how would the cultures have evolved differently?…We tried to come up with cultural axioms for each house so each looks different and they bear a cultural patina like our cultures do here on Earth." https://trekmovie.com/2017/08/03/stlv17-designers-explain-why-star-trek-discovery-klingons-are-bald-and-more/

From Star Trek News.Net

"What can you say to reassure us that we’re not losing the Klingons we know and love?” a furtive audience member asked during the Q&A portion. Mitchell assured the crowd that the recent publicity still image released was of one Klingon, from one house. “We will see all 24 houses and the leaders among them,” he revealed. The houses will be explored, and the physical and ideological differences between them. L’Rell is part of two houses, Chieffo explained, and the conflicts arising therein, as well as how she is viewed by the Federation versus her own people, will be explored in depth."http://www.treknews.net/2017/08/03/star-trek-discovery-cast-klingon-houses-stlv/

Here are a couple Promotional and Episode 1.01 Images from one predominant house featured in the first two episodes.There is an Albino character among them and in 1.02 (which I have not yet found a screencap/image for) one can see other houses and variations in holographic communication discussion.