The images do not show enoughof the climbing hydrangea leaves so I will
mention what I was thinking of so you can pursue this further...

* if it repeats every year at this time, it is possible that it is
caused by sunscald. Meaning, they may be getting more sun than you
think. A way to confirm this is to observe if the leaf lesions occur
only/mostly on leaves in direct contact with the sun. This way, leaves
that are protected and inside the inner part of the vine, they would
look fine. When investigating sunscald, one also has to look for sources
of indirect sun from wall, cement surfaces and windows in other
structures/buildings.

* there may be pests at work (caterpillars, spider mites are common this
time of the year) but you have to look during the day and at night
(many are nocturnal). Look at the top of the leaves and bottom of the
leaves. stems, rocks, soil, etc. However, some pests do the damage and
then leave so unless you catch them in the act, they may difficult to
identify. I could not see the underside of leaves to check for
caterpillars or spider mites.

* leaf spots are common during the summer although they usually show up
mid to late summer. They are fungal infections and you can see fungi
with a magnifying glass but I could not tell from the images.

I thought if it may be a lack of water but hydrangea leaves normally brown out from the edges inwards if they are in need of water to too much time.

If it is unsightly but does not spread and you do not see dieback, I
would not worry too much but I would monitor for changes every 2-4
weeks. If it is sunscald, the longest day of the year is behind us now
so we are now getting less sun every day so sunscald may be reduced.
However, I do not expect the partially browned out leaves to turn
completely green again. You can cut the petiole string of the worst
looking leaves if it bothers but remember that while they are green, the
leaves are producing food and sending it to the roots so do not cut a
lot of leaves.