I cannot figure out what tense this verb is at, can you help ? 

Here is the sentence : 

Itilaf Devletleri 30 Ekim 1918´de Osmanli Devleti ile birlikte imzaladıkları (...)

Teşekkür ederim !

imzala|dık|ları = verb stem + participle marker + possessive suffix pl 3rd

I think it is a dik-participle that means ´which the Allies signed together with the Osman state´. The whole structure acts as an attribute to the following word which could be anlaşma ´agreement´ or something similar.

This was a learner´s guess.

Good guess. That must be it!

If you say so.