"Istanbul has grown so much while I was not here."
Translation:Ben burada değilken İstanbul çok büyümüş.
If there is a verb in the expression, you should always add the "-ken" suffix after the verb. And you cannot use the -ken suffix with a vowel before it, in this situation, you should add "-y" before the "-ken". Some examples are: burada+y+ken, burada yaşıyor+ken, burada değil-ken, seninle+y+ken etc...
The sentence consists of three parts. [İstanbul] [ben burada değilken] [çok büyümüş.] You are probably confused because of "while I WASN'T here..." The difference is, in English it is a compound sentence while in Turkish it is is a basic sentence. There is only one predicative in basic Turkish sentence and it's not "değilken" but "çok büyümüş." So the latter is the one that has to be conjugated.