Index: clang-tidy/misc/DefinitionsInHeadersCheck.cpp
===================================================================
--- clang-tidy/misc/DefinitionsInHeadersCheck.cpp
+++ clang-tidy/misc/DefinitionsInHeadersCheck.cpp
@@ -104,8 +104,8 @@
     // Function templates are allowed.
     if (FD->getTemplatedKind() == FunctionDecl::TK_FunctionTemplate)
       return;
-    // Function template full specialization is prohibited in header file.
-    if (FD->getTemplateSpecializationKind() == TSK_ImplicitInstantiation)
+    // Ignore instantiated functions.
+    if (FD->isTemplateInstantiation())
       return;
     // Member function of a class template and member function of a nested class
     // in a class template are allowed.
@@ -131,7 +131,8 @@
     // Static data members of a class template are allowed.
     if (VD->getDeclContext()->isDependentContext() && VD->isStaticDataMember())
       return;
-    if (VD->getTemplateSpecializationKind() == TSK_ImplicitInstantiation)
+    // Ignore instantiated static data members of classes.
+    if (isTemplateInstantiation(VD->getTemplateSpecializationKind()))
       return;
     // Ignore variable definition within function scope.
     if (VD->hasLocalStorage() || VD->isStaticLocal())
Index: test/clang-tidy/misc-definitions-in-headers.hpp
===================================================================
--- test/clang-tidy/misc-definitions-in-headers.hpp
+++ test/clang-tidy/misc-definitions-in-headers.hpp
@@ -71,6 +71,12 @@
 template <typename T>
 int CB<T>::a = 2; // OK: static data member definition of a class template.
 
+template class CB<int>; // OK: explicitly instantiated static data member of a class template.
+inline int callCB() {
+  CB<double> cb; // OK: implicitly instantiated static data member of a class template.
+  return cb.a;
+}
+
 template <typename T>
 T tf() { // OK: template function definition.
   T a;
@@ -107,6 +113,12 @@
 
 int f8() = delete; // OK: the function being marked delete is not callable.
 
+template <typename T>
+int f9(T t) { return 1; }
+
+inline void callF9() { f9(1); } // OK: implicitly instantiated function.
+template int f9(double); // OK: explicitly instantiated function.
+
 int a = 1;
 // CHECK-MESSAGES: :[[@LINE-1]]:5: warning: variable 'a' defined in a header file; variable definitions in header files can lead to ODR violations [misc-definitions-in-headers]
 CA a1;