Postgres 9.6

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create table mytable (
  col jsonb
);

insert into mytable values
('{ "studentId":"123", "contact":{ "name":"parent1", "address":"address1"} }');

INSERT 0 1

UPDATE mytable
SET col = col - 'contact' || jsonb_build_object('guardian', jsonb_build_array(col->'contact'))

UPDATE 1

select *
from mytable

col

{"guardian": [{"name": "parent1", "address": "address1"}], "studentId": "123"}

SELECT 1