The most common and most likely answer to this crossword clue is the 7 letter word REALIZE
I've seen this crossword clue in The Daily Telegraph
R
E
A
L
I
Z
E
More clues leading to the result REALIZE
Buddy explains!
The straight part
We know that "Feel strongly" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case feel strongly = realize.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 REALIZE mean?
REALIZE verb- To make real; to convert from the imaginary or fictitious into reality; to bring into real existence
- To become aware of (a fact or situation, especially of something that has been true for a long time).
- To cause to seem real; to sense vividly or strongly; to make one's own in thought or experience.
- To acquire as an actual possession; to obtain as the result of plans and efforts; to gain; to get
- To convert any kind of property into money, especially property representing investments, such as shares, bonds, etc.
- To convert into real property; to make real estate of.
- To turn an abstract linguistic object into actual language, especially said of a phoneme's conversion into speech sound.