On Jayce Ready trigger, can I place a Trinity Force on a unit at a battlefield if I have in base "Jax Unmatched" to double hold?

Yes. You can play Trinity Force from hand as a Reaction on Jayce's ready trigger (a Closed State) and attach it to a unit at a battlefield, and the unit will then double-hold.

Jax, Unmatched grants all your Equipment Quick-Draw "everywhere," so Trinity Force has [Reaction] plus "When you play it, attach it to a unit you control." Quick-Draw's auto-attach has no location restriction — the gear's location simply becomes the unit's (Rule 434.4), and gear attached to a unit at a battlefield is legal (Rule 152.2). Pay only the play cost; the attach is free (FAQ #1989).

Once attached, Trinity Force's effect text ("When I hold, score 1 point") is appended to the unit's rules text (Rule 434.1.c). So when that unit holds, you score the battlefield's hold point plus Trinity Force's point — and the unit's own hold trigger still fires too.

Two notes: play it from hand (Quick-Draw doesn't attach gear already on the board, and you can't use Equip at Reaction speed — FAQs #10839, #9085), and make sure the attachment happens before the Beginning Phase hold. Jayce's trigger itself is unaffected — it's just your timing window.