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18a. My shop completed by a loving a daughter. _O_D_L_A - BORDELLA (brthel) ? Why?

I suspect it is Cordelia.

My = Cor
shop= deli
a=a
Cordelia was King Lear's daughter.

cor (my + deli (shop) + a .... daughter of King lear

Thanks guys, should have got that

Last one, 54a. US agent managed to turn round business N_R_O. My thinking takes me to RAN (managed) turn around NAR + CO (business) = NARCO?

Hope someone can help me go to bed a happy man.

Yes, a Narco is an US agent, dealing with narcotics.

Ah well, I'll sleep soundly now

Cheers Malone

Probably a mistake on my part adding these to a thread for 31a.

Help appreciated parsing these....

13a. Losing head, alien foe turned on a wolf (5) - AKELA (Wolf)

33a. General direction, briefly, infantry must receive check for disease (6,4) - TRENCH FOOT (Infantry disease)

3d. Some special skill winds prayer period up (5,6) - TRADE SECRET (Special skill)

25d. Insulting term Old Bill received: "dummy"? (7) - PLACEBO (Dummy?)

55a. Retiring collection? (9) - Is it NIGHTGEAR or NIGHTWEAR?

13a A [D]alek.
25d Pleb O plus Ac.
I'd go with nightwear - just my opinion.