Which will get priority- irule or LTM policy?

LTM Local Traffic Policy is executed and evaluated first, then the iRule

On another note, if your Local Traffic Policy is done with choosing a destination pool, it may not be where the requests will actually be routed to. Once the iRule is processed, and the outcome of destination pool selection is different, then the last choice is what matters. Effectively, an iRule can over-ride the decisions that were made by the LTM Policy. If you can, try to keep all pool-selection stuff in LTM Local Traffic Policy (or in iRule, if the functionality of LTM policy is insufficient for your scenario).

In your case, a configuration where persistence iRule is used on top of a pool-selection LTM policy should work without any problems.