Can Hunt keyword active when my unit died in cleanup phase?

No. Hunt does not trigger when your unit dies.

Hunt is defined as "When I Conquer or Hold, my controller gains X XP" (Rule 823.1.c.1). It triggers on establishing control of a battlefield, not on death. Dying during cleanup is a Kill event, not a Conquer or Hold event — that's what Deathknell is for.

The only connection between Hunt and cleanup is incidental: if your unit with Hunt successfully conquered a battlefield earlier in the same turn, the Hunt trigger would already be on the chain or have resolved — its death during a later cleanup does not prevent that trigger from resolving. But the death itself does not activate Hunt.