PSALM FIFTY-ONE, Gifts to ask for.

Psalm 51 RSV
10 Create in me a clean heart, O God,
        and put a new and right spirit within me.
11 Cast me not away from thy presence,
        and take not thy Holy Spirit from me.
12 Restore to me the joy of thy salvation,
        and uphold me with a willing spirit.

Psalm 51:11 reveals that the Holy Spirit is the active agent of God the Father in accomplishing His purposes.
In this instance the reference might be to God's anointing and The Holy Spirit's enabling for the individual.
It may refer to The Holy Spirit's role in clensing the inner life by opening spiritual eyes and ears (Ezek 3:27).
Also EZEKIEL 36:27  I will put my Spirit within you and cause you to walk in my statutes and be careful to obey my rules.  ESV

Gifts to pray for in Psalm 51:10,11,12;-
a pure or clean heart
inner renewal
a steadfast/right spirit within
retention of The Holy Spirit and the presence of God
the joy of salvation
a willing spirit ( to uphold )
and a spirit of fervor ( to sustain. )