Sailor runs into sea, extremely eager (7)
I believe the answer is:
mariner
'sailor' is the definition.
(mariner means a sailor)
'runs into sea extremely eager' is the wordplay.
'runs' becomes 'r' (cricket abbreviation).
'into' means one lot of letters goes inside another.
'sea' becomes 'main' (synonyms).
'extremely' says to hollow out the word (remove centre letters) (letters on the extremes of the word are used).
'eager' with its middle taken out is 'er'.
'r' going within 'main' is 'marin'.
'marin'+'er'='MARINER'
(Other definitions for mariner that I've seen before include "Probe" , "Jack" , "collier?" , "Sea-goer, ancient in the poem" , "Sea dog" .)