Why did Jamal kill this person?

Jamal essentially accepted the fact that the Sheik would survive and expose him as the culprit, losing all esteem, power and ultimately solidifying his notoriety as a bad person. Jamal used this pending loss as a means to escape his reality (leaving to the maldives), essentially a moment of weakness for someone so power hungry. Once he learns the death of the Sheik he no longer "needs" to flee and has found a new lease on the role as President. By killing Katerina, he literally and metaphorically removes any inkling of weakness or reminder of his weak moment in giving up the presidency and fleeing.

Bassam killing the Sheik, by wanting to be loyal to his brother, reinstated the ruthlessness in Jamal just as he was close to reaching a turning point for the better on a personal, psychological and emotional level. Katerina dying represents any hope for Jamal choosing the "good side".

Just my perspective on it. :)

Distressed, he invites Katerina to come with him instead and she agrees. However Bassam calls and informs him he did kill the Sheikh, and Jamal, to cover up any evidence he was thinking of giving up the Presidency, kills Katerina.

http://tyrantfx.wikia.com/wiki/Jamal_Al-Fayeed

Final paragraph.