A foundation, as exists at Birkenhead (5)
I believe the answer is:
basis
'a foundation' is the definition.
(I know that foundation can be written as basis)
'as exists at birkenhead' is the wordplay.
'exists' becomes 'is' (if something 'is', it exists).
'at' means one lot of letters go next to another (I've seen this in other clues).
'birkenhead' becomes 'b' (head letter of 'birken').
'as'+'is'='asis'
'asis' put after 'b' is 'BASIS'.
(Other definitions for basis that I've seen before include "Foundation or support, or a main principle" , "Foundation, fundament" , "Foundation of a theory or process" , "grounds" , "Ground, foundation" .)