Update parts of daterange

You can use overlapping &&, containment @> and difference - daterange operators to target specific records based on their relation to the incoming range.
The example you showed suggests you're following these rules:

• If an existing range is fully contained in the incoming one, you simply update its price.
  Example (2, '[2027-01-01,2028-01-01)', 234)
  becomes (2, '[2027-01-01,2028-01-01)', 567)
• If an existing range partially overlaps the incoming one, you split it so that the overlap becomes a new record with the new price, while the old one with the old price gets shortened. Example (2, '[2026-04-01,2027-01-01)', 123)
  splits into (2, '[2026-04-01,2026-04-15)', 123) _{(initial record, shortened to non-overlapping part)}
  and (2, '[2026-04-15,2027-01-01)', 567) _{(overlap with the new price)}
• It's not specified or demonstrated, but safe to assume that if the incoming range doesn't intersect any existing record, you just add it as a new one.

I'm using a prepared statement, but you can also wrap it in a routine to make it shareable and re-usable between sessions. _{demo at dbfiddle}

prepare addnewpricedaterange(daterange,decimal(12,2))as
with incomingchange(validat,price)as(values($1,$2)
),updatecontained as(
    update contract as c
    set price=i.price
    from incomingchange as i
    where i.validat @> c.validat
    returning new.*
),updateandreturnoverlaps as(  
    update contract as c
    set validat=c.validat-i.validat
    from incomingchange as i 
    where c.validat && i.validat
      and c.validat-i.validat  'empty'
    returning c.id
            , old.validat-new.validat as remainderrange
            , i.price
),insertindividualremainders as(
    insert into contract
    table updateandreturnoverlaps
),allintroducedranges as(
    select id
         , rangeagg(remainderrange) as allindividualremainders
         , price
    from(table updateandreturnoverlaps
         union all table updatecontained)
    group by id,price
),addpreviouslyundefinedranges as(
  insert into contract
  select id
       , unnest(datemultirange(validat)-allindividualremainders)
       , price
  from allintroducedranges
  join incomingchange
  using(price)
  returning*
)select 'completely new' as "source",* from addpreviouslyundefinedranges
 union all
 select 'fully covered', from update_contained
 union all
 select 'remainder from overlapped', from updateandreturnoverlaps;
execute addnewpricedaterange('[2026-04-15,2028-02-01)',567);

select ctid,* from contract order by validat;

Example covering a daterange without an existing price record:

execute addnewpricedaterange('[2025-01-01,2026-04-02)',42.42);

select ctid,* from contract order by validat;

Posting separately, as this proposes a schema change: if there's no real business logic requiring you to split records, or if you plan to merge them back together later, then you can make the PK deferrable:

PRIMARY KEY (id, validat WITHOUT OVERLAPS) deferrable initially deferred

prepare addnewpricedaterange(int,daterange,decimal(12,2))as
with incomingchange(id,validat,price)as(values($1,$2,$3)
),removecontained as(
    delete from contract as c
    using incomingchange as i
    where i.validat @> c.validat
      and i.id=c.id
),updateoverlapping as(  
    update contract as c
    set validat=c.validat-i.validat
    from incomingchange as i 
    where c.validat && i.validat
      and c.validat-i.validat  'empty'
      and i.id=c.id
)insert into contract table incomingchange;
execute addnewpricedaterange(2,'[2026-04-15,2028-02-01)',567);
select ctid,* from contract order by validat;