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Oh dear, totally beaten by three this week. All help will be very gratefully received!
16A Declines financial assistance, one I rejected.(8) -U-S---S
7D Displaced an older man.(7) L-O----
13A Without undue delay, avoiding a poisoner.(3) --P

Subsides

16, Subsid(i)es.

7 Leonard

7, Leonard.

13 Asp

AS[A]P

As(a)p.

SUBSIDES
Financial assistance is SUB AIDES without one (A) gives the answer

LEONARD - anagram of older man

As Soon As Possible = ASAP without A leaves ASP - a poisonous snake

Thank you very much everyone!