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Not sure about parsing these:
15a. It suggests cleric following it only gets worse (7,6)
A: Vicious circle.
Can't see how the first part fits.
19a. Brief address of surgeon is going around in May (5, 8)
A: Prime minister.
Prime = brief I suppose, but what's the "address of surgeon" doing?
4. Staff in NY opera house love souvenir (7)
A: Momento.
Staff = men, inside MO for the NY opera house and the final "o" for love. Where does the "t" come from?

15. It suggests implies the answer could give be the rest of the clue as definition. Vicious as an anagram indicator circle => cleric.
19. Surgeon is known as Mister, round in.
4. Met is the NY opera house, love = o.

4 memento = souvenir
NY opera house = the MET
staff = men + o (love)

Thank you.