Oracle 11g Release 2

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BANNER
Oracle Database 11g Express Edition Release 11.2.0.2.0 - 64bit Production
PL/SQL Release 11.2.0.2.0 - Production
CORE 11.2.0.2.0 Production
TNS for Linux: Version 11.2.0.2.0 - Production
NLSRTL Version 11.2.0.2.0 - Production

with YourSampleData (Person, Entrance, Exit) as (
select 'One', to_date('09.08.2022', 'dd.mm.yyyy'), null 								from dual union all 	
select 'One', null								 , to_date('10.08.2022', 'dd.mm.yyyy')	from dual union all
select 'One', to_date('10.08.2022', 'dd.mm.yyyy'), null 								from dual union all 	
select 'One', null								 , to_date('13.08.2022', 'dd.mm.yyyy')	from dual union all
select 'Two', to_date('08.08.2022', 'dd.mm.yyyy'), null 								from dual union all 	
select 'Two', null								 , to_date('12.08.2022', 'dd.mm.yyyy')	from dual
)
select Person, evt_date as Entrance, exit_date as Exit
from (
    select Person, evt_date, evt
        , lead(case when evt = 2 then evt_date else null end, 1) 
            ignore nulls over(
                partition by Person 
                    order by evt_date, evt desc
            ) as exit_date
    from (
        select Person
            , nvl(Entrance, Exit) as evt_date
            , case when Entrance is not null then 1 else 2 end evt
        from YourSampleData
    ) t1
)t2
where evt = 1 /*filter out all the rows initially containing exit dates data*/
order by Person, Entrance
;

PERSON	ENTRANCE	EXIT
One	09-AUG-22	10-AUG-22
One	10-AUG-22	13-AUG-22
Two	08-AUG-22	12-AUG-22