Is it correct to say, the profits show improvement by time
Does it mean here that profits increase year after year?
The profits show improvement by time
This means, as time moves forward, profits improve.
The sentence above is not specific as to the interval of the time. You can say any of:
The profits show yearly improvement by time.
The profits show improvement yearly by time.
The profits show improvement by time yearly.
but then "by time" is redundant (because both "by time" and "yearly" modify "improvement" and "yearly" is already a time expression) and doesn't need to be in the sentence, unless you are emphasizing that there is an improvement by time rather than some other metric, such as by customer, etc.
If you say:
The yearly profits show improvement by time.
you are saying a set of yearly profits are steadily improving over a number of years. This is not redundant as "yearly" is qualifying "profits", not "improvement."