Yes. As long as these Clans are not playing in the same variation of the game it is allowed.

To illustrate that here are some examples:

a) Clan1 plays CS 5on5 Ladder, Clan2 plays Q3 TDM Ladder,
--> ALLOWED
b) Clan1 plays CS 5on5 MR12 Ladder, Clan2 plays CS 2on2 Ladder
--> ALLOWED
c) Clan1 plays CS 5on5 MR12 Ladder, Clan2 plays CS 5on5 CO Ladder
--> ALLOWED
d) Clan1 plays CS 2on2 Ladder, Clan2 plays CS 2on2 Amateur Series
--> ALLOWED
e) Clan1 plays CS 5on5 MR12 Ladder, Clan2 plays CS 5on5 MR15 Amateur Series
--> ALLOWED
f) Clan1 plays CS 5on5 MR12 Ladder, Clan2 plays CS 5on5 MR12 Ladder
--> NOT ALLOWED
g) Clan1 plays CS Pro Series, Clan2 plays CS 5on5 MR12 Ladder
--> ALLOWED
h) Clan1 plays CS Pro Series, Clan2 plays CS 5on5 MR15 Amateur Series
--> NOT ALLOWED

For exceptional cases the according rules of the specific game and league or an admin have to be consulted.