Yes, your PC (with Metatrader) should be running all the time for copy signal.
Alternatively - you can use MQL5 VPS (you can close your PC in case of MQL5 VPS.
Check the subscription procedure once again with detailed explanation:
How to Subscribe to MT4/MT5 Signal - new instructions
https://www.mql5.com/en/forum/189731 (MT4)
https://www.mql5.com/en/forum/336422 (MT5)

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should i keep the pc running to get SL/Tp from the signal provider ?
will i get new orders from signal provider if my pc is not open ?
thank you ;)