You can do this with a CASE statement.
Select Top 1000000 Case
    When DatePart(Month, tblAssetCustom.Warrantydate) >= 10 Then
    Cast(DatePart(Year, tblAssetCustom.Warrantydate) + 1 As nvarchar) + ' Q1'
    When DatePart(Month, tblAssetCustom.Warrantydate) <
    4 Then Cast(DatePart(Year, tblAssetCustom.Warrantydate) As nvarchar) + ' Q2'
    When DatePart(Month, tblAssetCustom.Warrantydate) >= 4 And
    DatePart(Month, tblAssetCustom.Warrantydate) < 7 Then Cast(DatePart(Year,
    tblAssetCustom.Warrantydate) As nvarchar) + ' Q3'
    When DatePart(Month, tblAssetCustom.Warrantydate) >= 7 And
    DatePart(Month, tblAssetCustom.Warrantydate) < 10 Then Cast(DatePart(Year,
    tblAssetCustom.Warrantydate) As nvarchar) + ' Q4'
  End As [warranty expiration],
  tblAssets.AssetID,
  tblAssets.AssetName,
  tsysAssetTypes.AssetTypename,
  tsysAssetTypes.AssetTypeIcon10 As icon,
  tblAssets.Lastseen
From tblAssets
  Inner Join tblAssetCustom On tblAssets.AssetID = tblAssetCustom.AssetID
  Inner Join tsysAssetTypes On tsysAssetTypes.AssetType = tblAssets.Assettype
Where tblAssetCustom.State = 1
Order By tblAssetCustom.Warrantydate