I have a personal pension plan and employer has a company pension plan open to employees.
Is the company scheme an occupational scheme or a PRSA. If your employer will match contributions up to some level then it would generally make sense to take advantage of these contributions and join the scheme.
Can I have a personal pension plan and contribute to company pension plan?
You can retain the personal pension plan and leave it invested but you cannot contribute to an occupational pension scheme and a personal pension scheme at the same time as far as I know.
Should I transfer my existing personal pension to a PRSA?
That depends on (a) whether or not that is possible under the PRSA rules (b) whether or not you can find a company willing to accept the inward transfer of a personal pension fund to a PRSA and (c) what advantages there may be in effecting such a transfer (e.g. lower charges, more flexibility etc.)
Should I continue to pay monthly premium to personal pension plan as well as contribute to new company pension plan?
As above I don't think that this is possible or at least that that you cannot claim tax relief on contributions to multiple pension plans.
Note that it is not unusual for people to accumulate multiple pension funds (e.g. personal, PRSA, occupational, buy out bonds etc.) over their working lifetime these days and is is not necessarily advantageous a priori to "merge" them unless the (cost, flexibility, fund choice, administrative ease etc.) advantages are clear.
Does this make sense to you?