You do not need to do anything. Your contributions will continue to be paid to the Québec Pension Plan, and your new employer will also make his contributions.
Your employer must inform Revenu Québec that you were hired. Revenu Québec will then notify Retraite Québec, so that your file can be modified.
Supplemental pension plans
If you change jobs, it is possible that you will no longer be an active member of your pension plan. You may be able to transfer your benefits to another savings instrument of your choice.
If you are a member of a multi-employer plan, that is, a pension plan in which several different employers participate, and you leave your employer for another one who participates in the same plan, your active membership in the plan does not end, and you will continue to accumulate benefits under the plan.