Sailor runs into sea, outwardly eager (7)
I believe the answer is:
mariner
'sailor' is the definition.
(mariner means a sailor)
'runs into sea outwardly eager' is the wordplay.
'runs' becomes 'r' (cricket abbreviation).
'into' means one lot of letters goes inside another.
'sea' becomes 'main' (synonyms).
'outwardly eager' becomes 'er' (I can't explain this - if you can you should believe this answer much more).
'r' going inside 'main' is 'marin'.
'marin'+'er'='MARINER'
(Other definitions for mariner that I've seen before include "Jack" , "See 13" , "Bluejacket" , "Sea-goer, ancient in the poem" , "Person sailing" .)