Intercession of Christ
Christ's priestly office consists of these two parts, (1) the offering up of himself as a sacrifice, and (2) making continual intercession for us.
When on earth he made intercession for his people (Luke 23:34; John 17:20; Hebrews 5:7); but now he exercises this function of his priesthood in heaven, where he is said to appear in the presence of God for us (Hebrews 9:12, 24).
His advocacy with the Father for his people rests on the basis of his own all-perfect sacrifice. Thus he pleads for and obtains the fulfilment of all the promises of the everlasting covenant (1 John 2:1; John 17:24; Hebrews 7:25). He can be "touched with the feeling of our infirmities," and is both a merciful and a faithful high priest (Hebrews 2:17, 18; 4:15, 16). This intercession is an essential part of his mediatorial work. Through him we have "access" to the Father (John 14:6; Ephesians 2:18; 3:12). "The communion of his people with the Father will ever be sustained through him as mediatorial Priest" (Psalm 110:4; Revelation 7:17).
Intercession of the Spirit
(Romans 8:26, 27; John 14:26). "Christ is a royal Priest (Zechariah 6:13). From the same throne, as King, he dispenses his Spirit to all the objects of his care, while as Priest he intercedes for them. The Spirit Acts for him, taking only of his things. They both act with one consent, Christ as principal, the Spirit as his agent. Christ intercedes for us, without us, as our advocate in heaven, according to the provisions of the everlasting covenant. The Holy Spirit works upon our minds and hearts, enlightening and quickening, and thus determining our desires 'according to the will of God,' as our advocate within us. The work of the one is complementary to that of the other, and together they form a complete whole.", Hodge's Outlines of Theology.