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Help appreciated parsing these.....

15a He leaves bay, possibly, with popular old duke (6) - ORSINO (Duke)

45a It puts off easing tension, mostly involving fall from grace (9) - DETERRENT (It puts off)

ORS IN O
Bay, possibly = HORSE, minus HE + IN, popular, + O, old

DET ERR ENT
easing tension, mostly = DETENTE, minus E around ERR, fall from grace

That's brilliant, many thanks Mattrom.