Covenant theology is an interpretive framework for understanding the overall flow of the Bible. It is the mega picture of how God is dealing with the elect under the covenant of Grace.
Disensationalists commonly refer to Covenant Theology as replacement theology. This is generally rejected by Covenant Theologians. Covenant Theology stresses the unity of scripture, not changes. Covenant theologians would think of the "one people of God (Eph 2).
Certain events in the Bible would be seen differently by Dispensationalists and Covenant Theologians, such as Pentacost. Dispensationalists would say Pentacost is "the beginning of the Church" and the "Rapture" is the end of the Church. Then they would point at the time of Israel and the Kingdom as times for "Israel." Dispensationalists stress diversity.
Covenant Theologians of course see some changes at Pentacost. The prophetic New Covenant is fulfilled but this does not create a whole new and separate people of God, who are not connected to Old Testament promises. Just the opposite, we are connected to the OT promises of Israel, and as such, we are Israel. When we celebrate communion, our pastors hold up a cup and say "this is the new covenant in my blood." (Of course dispensational pastors do the same).
I should say that the lines between Covenant Theology and Dispensationalism are being blurred by some Theological movements since about 1990 or even earlier. On the Covenant side there is something called "New Covenant Theology." On the dispensational side there is something call "progressive dispensationalism."
Unfortunately, this whole discussion of Covenant Theology and Dispensationalism is filled with pejoratives, ad hominems, and misrepresentations. Be cautious of the way each group describes the other. I could mention the specifics of this, but it might be more profitable just to leave the specifics out of it (I actually wrote the specifics in this paragraph, but deleted it). May God be with you as you explore the issue.
