In a "that clause" following the verb "suggest" you could either use a present or past form:
Note that it's possible to either bring or not a "should" in your "that clause", as "should" is preferred in BrE
- He suggests that we should study hard.
- He suggested thst we studied (OR, should study) hard.
But note that, with "suggest" you shouldn't use an "indirect object":
- I suggest that they should be frank.
- I suggest that they be frank.
Hope this works...
- They suggested a new theatre to us. (correct)
- They suggested us a new theatre. (incorrect)
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