Police will have the pictures enlarged in an attempt to identify the thief.
This sentence include two tenses. The former one is will for the future tense and the other is past perfect future tense. How can it happen and what’s the grammar behind it?
There is no such thing as a “past perfect future tense.”
You are confusing the future perfect — you will have done something — with the future of have used as a causative verb — you will have something done. Note the word order: in a causative use, the participle or infinitive follows the object.
He will have to have three teeth filled.
She’s having her house painted in bright colors.
The director had them wait in the outer office.
This is the future perfect:
No matter how simple the first structure of your home may be, in a few years all settlers will have enlarged and beautified their dwellings. — Lawrence Solomon, Toronto Sprawls: A History, 2007.
By a certain time (in a few years) a certain state resulting from an action will have occurred (enlargement and beautification of their dwellings).
This is the future of have as a causative:
Competition finalists were awarded certificates and will have their photos enlarged and framed… Berwickshire News, 30 Mar. 2015.