Short answer
Before anything else, it may simply be late. A long list of perennials need weeks of warm soil before they show any growth, and some are not up until June, so a bare patch in April is not evidence of a dead plant. Once it is genuinely late for your area, the next things worth checking are how deep the crown was planted, whether mulch is sitting against it, and whether the plant was rated for winter where you live.
Listed in the order they are worth ruling out. It is normal for more than one of these to be happening at once, so work down the list rather than stopping at the first match.
This is first on the list because it is the one where acting too soon does the damage. A long list of perennials need several weeks of warm soil and warm air before they show anything above ground, and some are not up until June, so a bare patch in April is not evidence of a dead plant.
What to check first
Scratch the soil away from the base with a finger and look at the crown where the stems meet the roots. Firm, with pale buds or shoots forming, means it is on its way. Brown and mushy means it is not.
You can rule this in or out in under a minute, and it is a common beginner error with a published mechanism behind it. A perennial set too low in the ground, or with mulch heaped against its crown, is carrying a crown rot risk through the whole winter.
What to check first
Pull the mulch back from the base of the plant and look at where the stems meet the roots. That crown should sit at soil level with a ring of clear ground around it, not buried and not covered.
This is the fastest one to settle, and the answer is often that nothing you did was wrong. Hardiness zones exist precisely because a plant that thrives in one part of the country will not survive the winter in another.
What to check first
Enter your ZIP code on the USDA Plant Hardiness Zone Map to get your zone, then compare it against the zone printed on the plant tag or the nursery listing you bought from.
Worth checking against the species before concluding that anything went wrong. A number of very common garden perennials decline and disappear after a few good years, and that is their normal lifespan rather than a failure.
What to check first
Look up what you planted against the short lived list. Columbine, delphinium, lupine, blanket flower, Shasta daisy, coral bells and pinks are all on it.
This one only comes into play if you planted last autumn, and only where the ground freezes hard. A perennial that did not get its roots established before winter goes into the cold weaker, and it is the one most likely to be pushed out of the ground.
What to check first
Think back to when it went in, then look at the spot for a plant sitting proud of the soil with roots showing at the surface. A crown lifted clear of the ground is frost heaving and it is visible at a glance.
This one matters most for dry country plants growing where winters are wet. Soil that stays saturated through the cold months lowers a plant's winter hardiness, so something that would have survived the temperature does not survive the combination.
What to check first
Go and look at the spot a day or two after heavy rain. Standing water, or soil still soggy long after the rest of the bed has drained, is the condition described here.
Still not sure
This is exactly what your county Extension office answers, for free. They are the local horticulture experts for your area, they know what is going around this season where you live, and they will look at a photo.
Find your local Extension officePollinator Patch gives you watering and seasonal care for the plants you already own, written for your region rather than for gardening in general.