Meaning of the expression "labour under another "

Solution 1:

Psychologists work under the influence of another (rather severe) handicap in writing an autobiography.

(Presumably some first handicap has already been mentioned or alluded to in the context.)

Solution 2:

Here's something that might help -

Labour under [something]

: [labour under something] to exist or try to live in a situation where there are serious difficulties or problems.

Example sentence -

"Many countries labour under a huge burden of debt they cannot even begin to pay."

(From Macmillan Dictionary)

Solution 3:

"Labour under another" is not an expression; you are misunderstanding the sentence construction. The writer says that psychologists who are writing their autobiography suffer one more handicap (having presumably already mentioned one) which is rather severe.