I managed to grasp a new, initially indecipherable language (7)
I believe the answer is:
iranian
'language' is the definition.
(Iranian is an example)
'i managed to grasp a new initially indecipherable' is the wordplay.
'managed' becomes 'ran' (both can mean organised or was in charge of).
'to grasp' means one lot of letters goes inside another.
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'initially' indicates taking the first letters.
The first letter of 'indecipherable' is 'i'.
'a'+'n'+'i'='ani'
'ran' placed around 'ani' is 'ranian'.
'i'+'ranian'='IRANIAN'
(Other definitions for iranian that I've seen before include "Asian citizen" , "Foreign national" , "foreigner" , "from the Middle East" , "Eg, native of Tehran" .)