The most common and most likely answer to this crossword clue is the 4 letter word POPS
P
O
P
S
Buddy explains!
The straight part
We know that "The old man/is bursting" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case the old man/is bursting = pops.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 POPS mean?
POPS noun- (usually as a form of address) Father, dad.
- (usually as a form of address, by extension) A man old enough to be the speaker's father.
- A loud, sharp sound as of a cork coming out of a bottle.
- (Midwest US) An effervescent or fizzy drink, most frequently nonalcoholic; soda pop.
- (Midwest US) A bottle, can, or serving of effervescent or fizzy drink, most frequently nonalcoholic; soda pop.
- A pop shot: a quick, possibly unaimed, shot with a firearm.
- (in the phrase "a pop") A quantity dispensed, a portion, apiece.
- Something that stands out or is distinctive, especially to the senses.
- The removal of a data item from the top of a stack.
- A bird, the European redwing.
- The sixth derivative of the position vector with respect to time (after velocity, acceleration, jerk, jounce, crackle), i.e. the rate of change of crackle.
- A pistol.
- To make a pop, or sharp, quick sound.
- To burst (something) with a popping sound.
- (with in, out, upon, etc.) To enter, or issue forth, with a quick, sudden movement; to move from place to place suddenly; to dart.
- To place (something) (somewhere); to move or position (something) with a short movement.
- (often with over, round, along, etc.) To make a short trip or visit.
- To stand out; to be distinctive to the senses.
- To hit (something or someone).
- To shoot (usually somebody) with a firearm.
- To ejaculate.
- To remove (a data item) from the top of a stack.
- To remove a data item from the top of (a stack).
- To pawn (something) (to raise money).
- To swallow or consume (especially a tablet of a drug, sometimes extended to other small items such as sweets or candy).
- To perform (a move or stunt) while riding a board or vehicle.
- (of the ears) To undergo equalization of pressure when the Eustachian tubes open.
- Affectionate form of father.
- (Russian Orthodoxy) A Russian Orthodox priest; a parson.