The most common and most likely answer to this crossword clue is the 7 letter word CLAMPED
I've seen this crossword clue in The Daily Telegraph
C
L
A
M
P
E
D
Buddy explains!

The straight part
We know that "Firmly grasped" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case firmly grasped = clamped.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does CLAMPED mean?
CLAMPED verb- To fasten in place or together with (or as if with) a clamp.
- To hold or grip tightly.
- To modify (a numeric value) so it lies within a specific range.
- To cover (vegetables, etc.) with earth.
- To tread heavily or clumsily; to clump or clomp.