Cultivate head of dogwood the first lady cut off (7)
I believe the answer is:
develop
'cultivate' is the definition.
(thesaurus)
'head of dogwood the first lady cut off' is the wordplay.
'head of' indicates taking the first letters.
'the first lady' becomes 'eve' (I've seen this before).
'cut off' becomes 'lop' (I've seen this before).
The initial letter of 'dogwood' is 'd'.
'd'+'eve'+'lop'='DEVELOP'
(Other definitions for develop that I've seen before include "'Grow, evolve (7)'" , "Become more advanced" , "Become larger or more mature" , "Unfold" , "Result" .)