Can I add compost on top of the mulch, natural cedar I think or should I remove the mulch first?
Mulch is meant to deter weeds, conserve moisture and can be a decorative element in the garden.
Certainly removing the mulch will allow you to work the compost into the soil. That will get the benefits of the compost into the soil and to the roots of the plants that much quicker.
If your mulch is meant to deter weeds, depending on the compost you choose, adding compost on top could defeat the purpose of that mulch as weeds can grow readily in some compost.
If your mulch is meant to be decorative, you would certainly need to remove it prior to adding compost.
Since natural cedar decays into soil after a couple gardening seasons, you may consider working both the compost and mulch into the soil followed by a new layer of mulch. This will help condition your soil’s texture while adding nutrients at the same time.
Here is a link that can help understand which mulch and/or compost to use.