SQL Server 2019

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create table tbl
(
	id		int,
	start_time	time(0),
	end_time	time(0)
)
insert into tbl values
(1,   '10:00:00',    '10:34:00'),
(2,   '10:38:00',    '10:52:00'),
(3,   '10:53:00',    '11:23:00'),
(4,   '11:24:00',    '11:56:00'),
(5,   '14:20:00',    '14:40:00'),
(6,   '14:41:00',    '14:59:00'),
(7,   '15:30:00',    '15:40:00');
7 rows affected

with rcte as
(
	select	*, grp_start = start_time
	from	tbl
	where	id	= 1

	union all

	select	t.id, t.start_time, t.end_time, 
		grp_start = case when datediff(second, r.end_time, t.start_time) <= 120
				 then r.grp_start
				 else t.start_time
				 end
	from	tbl t
		inner join rcte r	on	t.id	= r.id + 1
)
select	id = min(id), grp_start as start_time, max(end_time) as end_time
from	rcte 
group by grp_start


id
start_time
end_time


1
10:00:00
10:34:00

2
10:38:00
11:56:00

5
14:20:00
14:59:00

7
15:30:00
15:40:00

id	start_time	end_time
1	10:00:00	10:34:00
2	10:38:00	11:56:00
5	14:20:00	14:59:00
7	15:30:00	15:40:00