Better men succeeded in the Open (8)
I believe the answer is:
outdoors
'the open' is the definition.
(synonyms)
'better men succeeded' is the wordplay.
'better' becomes 'outdo' (to outdo is to beat or do better than).
'men' becomes 'OR' (military abbreviation for Other Ranks).
'succeeded' becomes 's' (genealogical abbreviation).
'outdo'+'or'+'s'='OUTDOORS'
'in' is the link.
(Other definitions for outdoors that I've seen before include "In the open air" , "abroad" , "Alfresco" , "Is that great?" , "Al fresco" .)