after conquering a battlefield can i pay 1 to put irelia trigger conquer ability on the stack even when the legen is already ready?

Yes. Irelia's "When you conquer, you may pay [1] to ready me" trigger still goes on the chain after you conquer, and you may choose to perform it and pay the 1 even if the legend is already ready.

The trigger condition ("when you conquer") has no requirement that she be exhausted, and the cost is just 1 energy — not "exhaust her." Per Rule 415.1.c, being told to ready an already-ready unit is a legal instruction that simply does nothing. So you can finalize the trigger, pay the 1, and on resolution "ready me" is a no-op.

One practical note: nothing about the legend actually becomes ready, so any "when I'm readied" or "when you ready" effects won't fire — you're just spending 1 energy (Rule 383.3.b.1, 415.1.c).