Fills that land on beat 1
Practice the return to the groove as part of the fill.
A fill is only useful in the song if you can return to the next section on time. Start with a short fill whose count you can say while playing, then include the bar after it in every repetition.
Start with two notes
In a straight 4/4 practice groove, play kick on 1 and 3, snare on 2 and 4, and hi-hat eighth notes. In the last bar of a four-bar phrase, keep the groove through "3 &", then replace beat 4 and its & with two snare notes: right, left. Resume the groove with kick and hi-hat on the next 1. Reverse the hand order if that suits your setup.
Say "3 & 4 & 1 & 2 &" through the change. The fill notes use the same eighth-note spacing as the groove. If the next 1 is late, keep both notes on the snare and slow down before moving them to toms.
Extend it deliberately
Once the two-note fill is comfortable, try four alternating sixteenth notes on beat 4: "4 e & a". Return on the next 1. The beat still lasts the same amount of time; there are now four notes inside it.
Record three bars of groove, the fill bar and two bars afterward. Listen for a shortened beat 4, a pause while reaching for the hi-hat, or a louder groove after the fill. Work on the transition that changed.
Choose a place in the arrangement
Listen to the singer and the band through the section boundary. A sustained chord may leave space for a fill, while a vocal pickup may already provide the movement. Confirm what the entrance needs at rehearsal. A transition can work with the groove continuing unchanged.