Let the rye work for you in the very early spring as it will be the first thing that starts growing again here in about 3-5 weeks. Then once it gets a little taller, say in mid-to-late April on into early-May and the clover underneath is starting to come on...mow the rye at a height that you are cutting off the top of the rye plant but not so low that you are scalping your new clover.
That one mowing is usually enough to kill it and then voila...there's your clover and you should be pretty weed free. Depending on timing, rains, etc, you may want to mow the rye another time, but a little rogue rye in your clover field will not hurt a thing, as the rye will grow like crazy in May and June and then die in July.
I have also heard of others that advocate spraying the rye/clover field with a gly mix, which will kill the rye a lot faster than it will kill the clover. I have not done it that way myself, but I think it could work fine as long as you don't go too heavy with the gly and toast your new clover.
Lastly, something I have done several times now...just let it be. The rye will grow like crazy in May and June and will be 5' tall and thick, providing nesting and brooding cover and the die off in late July or so. Boom! there's the greenest, lushest clover left that you could find. The downside of this approach is that the clover is not so much of a food source during May, June and July as it otherwise could be. The upside is that it is no brainer easy and provides cover as mentioned above.
Nowadays, I usually split the difference and leave and acre or two to "run wild" and mow an acre or two so there is fresh clover somewhere on the farm too.