COUNT after CROSS JOIN
It's probably easiest to add one correlated sub-query for each count:

SELECT D.*, S1.*, S2.*, S3.*
     , ( SELECT COUNT(1) FROM Group G WHERE G.&lt;key&gt; = ... ) as GroupCount
     , ( SELECT COUNT(1) FROM Client C WHERE C.&lt;key&gt; = ... ) as ClientCound  
FROM Districts as D
CROSS JOIN Seasons as S1
CROSS JOIN Sectors as S2
CROSS JOIN Sites as S3


Since I don't know how Group and Client relates to the other tables, I left that as an exercise for the reader ;-)

It's quite unusual to do a cartesian product between 4 tables in a query, but perhaps you have your reason for that. Beware that the cardinality of the result is the product of the cardinality for the individual tables. If the cardinality for the tables is 100, the result will contain 100^4=100000000 rows. For a cardinality of 1000, you end up with 1000^4=1000000000000. If each row is 1 byte, the result in the latter case is 1Tb.