Grow abundant in parts of the Thames river (6)
I believe the answer is:
thrive
'grow' is the definition.
(thriving is a kind of growing)
'in parts of the thames river' is the wordplay.
'in' is an insertion indicator.
'parts of' suggests taking the first letters (I've seen 'part' mean this).
'thames' becomes 'hive' (I am not sure about this - if you are sure you should believe this answer much more).
'river' becomes 'r'.
The initial letter of 'the' is 't'.
't'+'hive'='thive'
'thive' enclosing 'r' is 'THRIVE'.
'abundant' acts as a link.
I am not very happy about this link. It may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for thrive that I've seen before include "Grow vigorously, flourish" , "Do well, flourish" , "Develop well" , "Be successful" , "Succeed" .)