The most common and most likely answer to this crossword clue is the 5 letter word LADEN
I've seen this crossword clue in The Times
L
A
D
E
N
More clues leading to the result LADEN
- Left port carrying cargo
- Left port, carrying heavy cargo
- Young man being featured regularly in Loaded
- On port, head of logistics gets loaded
- Loaded in large Yemeni port
- Like a full ship that’s left port
- Left port heavily loaded
- On the way up earned a lot contracting, becoming loaded
- Cassady returned carrying bit of dope, loaded
- Some moaned aloud over being charged
Buddy explains!

The straight part
We know that "carrying heavy cargo" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case carrying heavy cargo = laden.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 LADEN mean?
LADEN verb- To fill or load (related to cargo or a shipment).
- To weigh down, oppress, or burden.
- To use a ladle or dipper to remove something (generally water).
- To transfer (molten glass) from the pot to the forming table, in making plate glass.
- To admit water by leakage.
- Weighed down with a load, burdened.
- Heavy.
- Oppressed.
- In the form of an adsorbate or adduct.