Database

[{"_id":1,"arr":[{"_id":11},{"_id":12}]},{"_id":2,"arr":[{"_id":21},{"_id":22}]}]

Query

db.collection.aggregate([{$match:{"_id":2}},{$project:{arr:{$filter:{input:"$arr",as:"ar",cond:{$eq:["$$ar._id",21]}}}}}])

Result