The most common and most likely answer to this crossword clue is the 7 letter word CLOSING
C
L
O
S
I
N
G
Buddy explains!

The straight part
We know that "Last" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case last = closing.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 CLOSING mean?
CLOSING verb- (physical) To remove a gap.
- (social) To finish, to terminate.
- To come or gather around; to enclose; to encompass; to confine.
- To have a vector sum of 0; that is, to form a closed polygon.
- The act by which something is closed.
- The end or conclusion of something.
- The final procedure in a house sale, when documents are signed and recorded.
- In morphology, the erosion of the dilation of a set.
- Pertaining to the finish or ending of a series of events; occurring at the end or after all others.