shorten the string to the desired values

You could treat [<>] as the word delimiter and take the second word:

with test (col) as
   ( select '<a href="https://help.company.ru/operator/#uuid:serviceCall$14612">INC102</a>'   from dual union all
     select '<a href="https://help.company.ru/operator/#uuid:serviceCall$146122">INC1020</a>' from dual union all
     select '<a href="https://help.company.ru/operator/#uuid:serviceCall$1461">INC10200</a>'  from dual
   )
select regexp_substr(col,'[^<>]+', 1, 2)
from   test;

REGEXP_SUBSTR(COL,'[^<>]+',1,2)
-------------------------------
INC102
INC1020
INC10200

Since I understand that "Substr" will not work here.

Says who?

SQL> with test (col) as
  2    (select '<a href="https://help.company.ru/operator/#uuid:serviceCall$14612">INC102</a>'   from dual union all
  3     select '<a href="https://help.company.ru/operator/#uuid:serviceCall$146122">INC1020</a>' from dual union all
  4     select '<a href="https://help.company.ru/operator/#uuid:serviceCall$1461">INC10200</a>'  from dual
  5    )
  6  select
  7    substr(col,
  8           instr(col, '>') + 1,
  9           instr(col, '<', instr(col, '>')) - instr(col, '>') - 1
 10          ) result
 11  from test;

RESULT
------------------------------------------------------------------------------------------------------------------------

INC102
INC1020
INC10200

SQL>

What does it do?

• lines #1 - 5: sample data
• line #8: starting point of the SUBSTR function is one character after the first > sign
• line #9: length (used as the 3rd parameter of the SUBSTR) is position of the first < that follows the first > minus position of the first >

And that's it ... why wouldn't it work?

If you just want to extract "INC" with the following digits, use regexp_substr():

select regexp_substr(link, 'INC[0-9]+')

Here is a db<>fiddle.