What is the priority of a phenyl group in a compound such as this?
For preferred IUPAC names, the ring is preferred to the chain.
Therefore, the preferred IUPAC name for the given structure is but-3-en-1-ylbenzene.

However, the context may favour the chain, so that, for example, an unsaturated acyclic structure may be recognized.

When one double bond is present, an unbranched alkene is named by changing the ending to ‘ene’. The double bond is assigned the lower locant possible, which is placed immediately in front of the ending ‘ene’. When several structural features appear, low locants are assigned to ‘ene’ endings before detachable alphabetized prefixes.
Therefore, a correct name for the given structure is 4-phenylbut-1-ene.