If opponent play promising future. And he banish elder dragon. I banish thousand tail watcher. How it will be resolved?

Yes — your Thousand-Tailed Watcher dies from Elder Dragon's play effect, and Elder Dragon sticks around at 7 Might for the turn.

Promising Future resolves completely first: you (the "next player") play Thousand-Tailed Watcher paying its 1 power, then your opponent plays Elder Dragon paying its 4 power. Both "when you play me" triggers go on the Chain after Promising Future finishes, resolving LIFO — so Elder Dragon's trigger resolves first and deals 1 damage to up to one enemy unit at each location, including your Watcher. Because Elder Dragon's passive makes any of its controller's damage lethal to enemy units, that 1 damage kills the Watcher regardless of its 7 Might (FAQ #8684; lethal-damage modification rule 323.5).

Then Watcher's trigger resolves and gives enemy units −3 Might this turn, reducing Elder Dragon from 10 to 7 — but that happens after the Watcher is already dead, so it doesn't save it. One caveat: Elder Dragon's play effect is "up to one" per location, so your opponent could choose not to target the Watcher if they want it to live.