There are several views of the covenants within the Reformed/Calvinist camp, broadly defined.
The traditional view is that the covenants are unified and that the New Covenant is new in the sense of "new and improved" rather than radically new (cf. Rom. 11 for how Gentiles are grafted into the continuing tree started with Abraham and in Gal. 3 how the law was added to the Abrahamic covenant). This view is held by conservatives in paedo-baptist circles such as Presbyterian, Dutch Reformed, Anglican, and non-denominational / Congregationalist churches (note: form of church government is not really an overlapping issue here but is a convenient way of identifying folks since they generally correlate). Examples: R.C. Sproul, J.I. Packer, Meredith Kline, most of the Puritans (e.g., those who wrote the Westminster Standards), etc. See An Old Testament Theology by Bruce Waltke and Christ of the Covenants by O. Palmer Robertson for recent examples of this view.
There are also many "young, restless and Reformed" types who are in credo-baptist circles, typically Baptist, Charismatic, and non-denominational (all of which are usually Congregationalist in their form of government, but like I said, that's a different matter). They typically see the New Covenant as replacing rather than being continuous with the Old Testament covenants. Sometimes they call their view "New Covenant Theology". Examples include John Piper, D.A. Carson, Albert Mohler, old-timer John Gill, etc. See Kingdom through Covenant: A Biblical-Theological Understanding of the Covenants by Gentry and Wellum for a recent example of this view.
As far as Arminians go, views also vary. Those who self-identify as classical Arminians can be pretty close to the traditional Reformed views on the Covenants, though not always. Some distinctions they draw between themselves and traditional Calvinists are that covenants are always conditional (see e.g., "An Arminian Covenant Theology").
Other Arminians are more distant from the traditional Calvinist view. They can be similar to the Reformed Baptist "New Covenant" view or be better categorized as Dispensational. (John MacArthur is an example of someone who is Calvinistic in his soteriology but a "leaky Dispensational" in his understanding of biblical history and the nature of the covenants.)
In short, I don't think there's a tidy division of people who advocate Calvinist vs. Arminian soteriology with those who advocate "traditional Covenant Theology" vs. "New Covenant Theology" vs. Dispensationalism (in any of its forms). There are some correlations, but they are not strong and there are a goodly number of outliers.