First, resolve closing or sealing gate.

Then,fight with monster?

or First, fight with the monster,

and close or seal a gate.

The investigator returns to Arkham from another world during the Movement phase and has an exemption from fighting any monsters at that location for that first movement turn only . Then during the Arkham Encounters phase, attempt to close/seal the gate. On the next turn, during the Movement phase, the monster will have to be dealt with (by evading or entering combat).

You know, there is entire part of rules, called "Monsterz guardin' gatez".

If an encounter sends you back to Arkham early, the turn will end before the next movement phase, so you won't get the exemption.