Head of state taken in by respectable pedigree (7)
I believe the answer is:
descent
'pedigree' is the definition.
('descent' can be a synonym of 'pedigree')
'head of state taken in by respectable' is the wordplay.
'head of' indicates taking the first letters.
'taken in by' means one lot of letters goes inside another.
'respectable' becomes 'decent' ('decent' can be similar in meaning to 'respectable').
The initial letter of 'state' is 's'.
's' placed inside 'decent' is 'DESCENT'.
(Other definitions for descent that I've seen before include "Ancestry - downward move" , "Derivation from an ancestor - going down" , "Roots" , "Lineage" , "Downward slope" .)