Update

syntax/basic/class.vim

@@ -15,7 +15,7 @@ syntax match   typescriptClassName             contained /\K\k*/
 
 syntax region typescriptClassTypeParameter
   \ start=/</ end=/>/
-  \ contains=typescriptTypeParameter
+  \ contains=@typescriptTypeParameterCluster
   \ nextgroup=typescriptClassBlock,typescriptClassExtends
   \ contained skipwhite skipnl
 
@@ -47,7 +47,7 @@ syntax match   typescriptInterfaceName             contained /\k\+/
   \ skipwhite skipnl
 syntax region typescriptInterfaceTypeParameter
   \ start=/</ end=/>/
-  \ contains=typescriptTypeParameter
+  \ contains=@typescriptTypeParameterCluster
   \ nextgroup=typescriptObjectType,typescriptInterfaceExtends
   \ contained
   \ skipwhite skipnl

syntax/basic/literal.vim

@@ -16,7 +16,7 @@ syntax region  typescriptString
   \ contains=typescriptSpecial,@Spell
   \ extend
 
-syntax match   typescriptSpecial            contained "\v\\%(x\x\x|u%(\x{4}|\{\x{4,5}})|c\u|.)"
+syntax match   typescriptSpecial            contained "\v\\%(x\x\x|u%(\x{4}|\{\x{1,6}})|c\u|.)"
 
 " From vim runtime
 " <https://github.com/vim/vim/blob/master/runtime/syntax/javascript.vim#L48>
@@ -24,7 +24,7 @@ syntax region  typescriptRegexpString          start=+/[^/*]+me=e-1 skip=+\\\\\|
 
 syntax region  typescriptTemplate
   \ start=/`/  skip=/\\\\\|\\`\|\n/  end=/`\|$/
-  \ contains=typescriptTemplateSubstitution
+  \ contains=typescriptTemplateSubstitution,typescriptSpecial,@Spell
   \ nextgroup=@typescriptSymbols
   \ skipwhite skipempty
 

syntax/basic/object.vim

@@ -2,9 +2,11 @@ if !exists('g:polyglot_disabled') || index(g:polyglot_disabled, 'typescript') ==
 
 syntax region  typescriptObjectLiteral         matchgroup=typescriptBraces
   \ start=/{/ end=/}/
-  \ contains=@typescriptComments,typescriptObjectLabel,typescriptStringProperty,typescriptComputedPropertyName
+  \ contains=@typescriptComments,typescriptObjectLabel,typescriptStringProperty,typescriptComputedPropertyName,typescriptObjectAsyncKeyword
   \ fold contained
 
+syntax keyword typescriptObjectAsyncKeyword async contained
+
 syntax match   typescriptObjectLabel  contained /\k\+\_s*/
   \ nextgroup=typescriptObjectColon,@typescriptCallImpl
   \ skipwhite skipempty

syntax/basic/type.vim

@@ -3,13 +3,17 @@ if !exists('g:polyglot_disabled') || index(g:polyglot_disabled, 'typescript') ==
 " Types
 syntax match typescriptOptionalMark /?/ contained
 
+syntax cluster typescriptTypeParameterCluster contains=
+  \ typescriptTypeParameter,
+  \ typescriptGenericDefault
+
 syntax region typescriptTypeParameters matchgroup=typescriptTypeBrackets
   \ start=/</ end=/>/
-  \ contains=typescriptTypeParameter
+  \ contains=@typescriptTypeParameterCluster
   \ contained
 
 syntax match typescriptTypeParameter /\K\k*/
-  \ nextgroup=typescriptConstraint,typescriptGenericDefault
+  \ nextgroup=typescriptConstraint
   \ contained skipwhite skipnl
 
 syntax keyword typescriptConstraint extends