SeriesData::scmp
An error occurs because the constant term in the second series does not match the expansion point of the first series:
ComposeSeries[Series[Cos[x], {x, 0, 3}], Series[x, {x, 1, 2}]]This shows a valid series composition:
ComposeSeries[Series[Cos[x], {x, 0, 3}], Series[x - 1, {x, 1, 2}]]