Adam Clarke on Psalms 51:10

Create in me a clean heart - Mending will not avail; my heart is altogether corrupted; it must be new made, made as it was in the beginning. This is exactly the sentiment of St. Paul: Neither circumcision availeth any thing, nor uncircumcision, but a new creation; and the salvation given under the Gospel dispensation is called a being created anew in Christ Jesus.

A right spirit within me - רוח נכון ruach nachon, a constant, steady, determined spirit; called Psa 51:12, רוח נדיבה ruach nedibah, a noble spirit. a free, generous, princely spirit; cheerfully giving up itself to thee; no longer bound and degraded by the sinfulness of sin.