Do I need to purchase display adhesive assembly when replacing battery

The pre-existing adhesive will be thoroughly damaged when you remove the screen. Technically speaking, you don't need to replace the adhesive, the phone will re-assemble fine and you will not see a difference. Apple was experimenting with the adhesive in preparation for the iPhone 7 which was rated as water-resistant.

However, if you replace the adhesive, you will not be able to achieve the same level of sealing as when it's done in the factory.

Full disclosure: I run a shop and I always replace the adhesive as a best practice. For DIY, it's not necessary but preferable.