Can I contribute to a 401k while receiving a pension? Will my contributions be deductible?

In 2023 I plan to quit work and start collecting my pension.  It wont be enough to live on so I plan to work after I quit where I am at right now.  The plan is either to take a job with less pay or work as an independent contractor.  I want to continue saving for my eventual retirement at 65, so I plan to contribute to a 401k at my future job.  I will be over 55 at that point.

 

Can I contribute to a 401k while receiving a pension?

Will my contributions be tax-deductible?