The AoP was pretty beat up after Gettysburg, so it took some time to get back to anything resembling respectable strength, in the eyes of Meade. The Mine Run and Bristoe Station campaigns involved both a Union forray to test Confederate strength, and a Confederate response in kind.
In September of 1863 Longstreet was sent to Chickamauga with two reinforced divisions resulting in the victory there and then Howard's corps was diverted from the AoP to support the Army of the Cumberland at Chattanooga (under Thomas at that point, Rosecrans having been relieved), and Sherman who was on his way from Mississipi. So aside from the Mine Run and Bristoe Station campaigns/battles, both Meade and Grant seemed content to settle into winter quarters, and await the consequences of the events in Chattanooga. Lee hoped to get Longstreet back, and Meade hoped for either Hooker's men or some substitute for them. But both Hooker and Longstreet were held up and unable to join their original forces for quite some time, Hooker was in Knoxville at Christmas 1863 before being relieved, and Longstreet went into winter quarters in N.E. Tennessee before re-joining Lee in the early spring.
Nothing was going to happen between December and early March anyway, the roads were in terrible shape due to alternate snow, rain, and thawing. So Grant wasn't needed until late March/early April, anyway.
Of course, just to make clear, Grant was in charge of all Union armies, not just the AoP. He had Lincoln's authority to remove Meade if he thought it advisable, but after meeting with Meade shortly after his arrival at AoP headquarters, Grant decided to keep him in command. He did, however, decide to place his headquarters with the AoP, where he could keep a close eye on Meede. If he replaced Meade, he would have had to put someone else in charge, which raised the ugly prospect of the Union army changing commanders after every major battle.