Setter welcoming public turning up old source of common heritage? (4,4)
I believe the answer is:
gene pool
'source of common heritage?' is the definition.
'setter welcoming public turning up old' is the wordplay.
'setter' becomes 'gel' (something which sets**).
'welcoming' means one lot of letters goes inside another (in sense of 'inviting in').
'public' becomes 'open' ('open' can be similar in meaning to 'public').
'turning up' shows that the letters should be reversed in order.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'open' written backwards gives 'nepo'.
'nepo'+'o'='nepoo'
'gel' going around 'nepoo' is 'GENE POOL'.
(Other definitions for gene pool that I've seen before include "All the DNA in a population" , "breeding stock" , "Sum of units of heredity in interbreeding population" .)