Cede most of county, no doubt at first with hesitation (9)
I believe the answer is:
surrender
'cede most' is the definition.
'surrender' can be an answer for 'cede' (synonyms). I'm not sure about the 'most' bit.
'county no doubt at first with hesitation' is the wordplay.
'county' becomes 'surre' (I can't justify this - if you can you should believe this answer much more).
'at first' indicates taking the first letters.
'with' means one lot of letters go next to another.
'hesitation' becomes 'er' (sound used when hesitating).
The initial letters of 'no doubt' is 'nd'.
'surre'+'nd'+'er'='SURRENDER'
'of' is the link.
Can you help me to learn more?
(Other definitions for surrender that I've seen before include "Yield to the control of another" , "Wave the white flag" , "Cede" , "Submit (to an opponent)" , "Cease resistance" .)