TL;DR
Just reindex it as other index using its index name:
REINDEX INDEX <indexname>;
MCVE
Let's create a table with a Primary Key constraint which is also an Index:
CREATE TABLE test(
Id BIGSERIAL PRIMARY KEY
);
Looking at the catalogue we see the constraint name:
SELECT conname FROM pg_constraint WHERE conname LIKE 'test%';
-- "test_pkey"
Having the name of the index, we can reindex it:
REINDEX INDEX test_pkey;
You can also fix the Constraint Name at the creation:
CREATE TABLE test(
Id BIGSERIAL NOT NULL
);
ALTER TABLE test ADD CONSTRAINT myconstraint PRIMARY KEY(Id);
If you must address concurrence, then use the method a_horse_with_no_name
suggested, create a unique index concurrently:
-- Ensure Uniqueness while recreating the Primary Key:
CREATE UNIQUE INDEX CONCURRENTLY tempindex ON test USING btree(Id);
-- Drop PK:
ALTER TABLE test DROP CONSTRAINT myconstraint;
-- Recreate PK:
ALTER TABLE test ADD CONSTRAINT myconstraint PRIMARY KEY(Id);
-- Drop redundant Index:
DROP INDEX tempindex;
To check Index existence:
SELECT * FROM pg_index WHERE indexrelid::regclass = 'tempindex'::regclass