The most common and most likely answer to this crossword clue is the 8 letter word INTEREST
I've seen this crossword clue in The Guardian
I
N
T
E
R
E
S
T
More clues leading to the result INTEREST
- Money to be made in half-term holiday
- Curiosity shown by soldiers in trial cases
- Stake money added to one's account
- Concern for butcher in Street
- Claim to participate in street dancing
- Pursuit of profit
- Popular setter aroused curiosity
- Bury the hatchet finally, suppressing second concern
- Setter in anagrams to excite curiosity
- Engage in experiment involving rattlesnake’s skin
Buddy explains!

The straight part
We know that "Engage" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case engage = interest.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 INTEREST mean?
INTEREST noun- The price paid for obtaining, or price received for providing, money or goods in a credit transaction, calculated as a fraction of the amount or value of what was borrowed.
- Any excess over and above an exact equivalent
- A great attention and concern from someone or something; intellectual curiosity.
- Attention that is given to or received from someone or something.
- An involvement, claim, right, share, stake in or link with a financial, business, or other undertaking or endeavor.
- Something or someone one is interested in.
- Condition or quality of exciting concern or being of importance
- Injury, or compensation for injury; damages.
- (usually in the plural) The persons interested in any particular business or measure, taken collectively.
- To engage the attention of; to awaken interest in; to excite emotion or passion in, in behalf of a person or thing.
- To be concerned with or engaged in; to affect; to concern; to excite.
- To cause or permit to share.